This project emphasizes the development and use of atomistic simulation tools ( quantum mechanics, molecular dynamics, statistical mechanics ) for characterizing, predicting, and designing materials with applications to biological, chemical, catalysis, polymer, semiconductor, and ceramic systems. A focus is upon extending the methodologies to apply atomistic theory to the most important industrial applications. This pushes available methods ( theory and software ) to the limit and stimulates the development of new theory and new software. In quantum chemistry the key methodological developments are (i) ab initio; combination of pseudospectral and many body methodologies to decrease the cost for obtaining wavefunctions of very large systems (up to 5000 basis functions) This involves GVB, GVD-RCI, CAS-SCF, MP2 type approaches where the localization inherit in GVB and in numerical grids is used to decrease the costs and scaling for large systems. For periodic boundary conditions (PBC) a duel space approach for the long-range Coulomb interactions is combined with P and GVB methodologies. (ii) Density functional theory: we focus on 3-D and 2-D periodic systems using Gaussian basis sets (rather than plane waves) and all-electron (rather than pseudopotentials). This requires the Gaussian Dual Space (GDS) approach to make it practical. In Molecular dynamics the key methodology developments are (i) the Cell Multipole method (CMM) for rapid accurate calculation of the long-range forces for very large systems [million atom finite systems (e.g. viruses) and million atom per unit cell periodic systems (e.g. amorphous polymers)]. (ii) the Newton-Euler Inverse Mass Operator (NEIMO) approach for internal coordinate dynamics of very large systems ( 100,000 degrees of freedom).